Keras. Prerequisites You must satisfy the following requirements:  Any kind of OS (Windows, Linux or Mac)  Python version 3.5 or higher. Python Keras is python based neural network library is always recommended to use a virtual environment while developing Python applications. Linux/Mac OS Linux or mac OS users, go to your project root directory and type the below command to create virtual Activate the environment This step will configure python and pip executables in your shell path. Linux/Mac OS Now we have created a virtual environment named “kerasvenv”. Move to the folder and type

Miniconda3-py39_4.12.0-MacOSX-x86_64.sh -b 如果我们使用Linux，假设Python版本是3.9（我们的测试版本），将下载名称包含字符串“Linux”的bash脚 本，并执行以下操作： # 文件名可能会更改 sh Miniconda3-py39_4.12.0-Linux-x86_64.sh -b 接下来，初始化终端Shell，以便我们可以直接运行conda。 一只猫、一只公鸡、一只狗、一头驴 学习预测不相互排斥的类别的问题称为多标签分类（multi‐label classification）。举个例子，人们在技术博客 上贴的标签，比如“机器学习”“技术”“小工具”“编程语言”“Linux”“云计算”“AWS”。一篇典型的文章可 能会用5～10个标签，因为这些概念是相互关联的。关于“云计算”的帖子可能会提到“AWS”，而关于“机 器学习”的帖子也可能涉及“编程语言”。 此外， 算能力却很弱。其次，数据集相对较小。事实上，费舍尔1932年的鸢尾花卉数据集是测试算法有效性的流行 工具，而MNIST数据集的60000个手写数字的数据集被认为是巨大的。考虑到数据和计算的稀缺性，核方法 （kernel method）、决策树（decision tree）和图模型（graph models）等强大的统计工具（在经验上）证明 是更为优越的。与神经网络不同的是，这些算法不需要数周的训练，而且有很强的理论依据，可以提供可预

PyTorch 中可以通过 Linear 类直接实现，特别地，当激活函数?为空时，全连接层也称为线性层。比如，通过 Linear 类创建输入 4 个节点，输出 3 个节点的网络层，并通过全连接层的 kernel 成员名查 看其权值矩阵?： In [45]: # 定义全连接层的输出节点为 3, 输入节点为 4 fc = nn.Linear(4, 3) fc.weight # 查看权值矩阵 # 创建 32x32 的彩色图片输入，个数为 4 x = torch.randn(4, 3, 32, 32) # 创建卷积神经网络 layer = nn.Conv2d(3, 16, kernel_size=3) out = layer(x) # 前向计算 out.shape # 输出大小 Out[48]: torch.Size([4, 16, 30, 30]) 其中卷积核张量 trainable_variables: print(p.name, p.shape) # 参数名和形状 Out[3]: dense_2/kernel:0 (4, 3) dense_2/bias:0 (3,) dense_3/kernel:0 (3, 3) dense_3/bias:0 (3,) Sequential 容器是最常用的类之一，对于快速搭建多层神经网络非常有用，应尽量多使

NVIDIA CUDA 11.4.2 with cuBLAS 11.6.5.2 1.10.0a0+0aef44c TensorRT 8.0.3.4 for x64 Linux TensorRT 8.0.2.2 for Arm SBSA Linux 21.09 NVIDIA CUDA 11.4.2 TensorRT 8.0.3 21.08 NVIDIA CUDA 11.4.1 1.10.0a0+3fd9dcf NVIDIA CUDA 11.4.2 with cuBLAS 11.6.5.2 1.10.0a0+0aef44c TensorRT 8.0.3.4 for x64 Linux TensorRT 8.0.2.2 for Arm SBSA Linux 21.09 NVIDIA CUDA 11.4.2 TensorRT 8.0.3 21.08 NVIDIA CUDA 11.4.1 1.10.0a0+3fd9dcf NVIDIA CUDA 11.4.2 with cuBLAS 11.6.5.2 1.10.0a0+0aef44c TensorRT 8.0.3.4 for x64 Linux TensorRT 8.0.2.2 for Arm SBSA Linux 21.09 NVIDIA CUDA 11.4.2 TensorRT 8.0.3 21.08 NVIDIA CUDA 11.4.1 1.10.0a0+3fd9dcf

activation=None, use_bias=True, kernel_initializer='glorot_uniform', bias_initializer='zeros', kernel_regularizer=None, bias_regularizer=None, activity_regularizer=None, kernel_constraint=None, bias_constraint=None) activation(dot(input, kernel) + bias) 其 中 activation 是按逐个元素计算的激活函数，kernel 是由网络层创建的权值矩阵，以及 bias 是 其创建的偏置向量 (只在 use_bias 为 True 时才有用)。 • 注意: 如果该层的输入的秩大于 2，那么它首先被展平然后再计算与 kernel 的点乘。 例 # 作为 Sequential • use_bias: 布尔值，该层是否使用偏置向量。 • kernel_initializer: kernel 权值矩阵的初始化器 (详见 initializers)。 • bias_initializer: 偏置向量的初始化器 (see initializers). • kernel_regularizer: 运用到 kernel 权值矩阵的正则化函数 (详见 regularizer)。

redefine ω by w = � s∈S αsy(s)x(s) where S denotes the set of the indices of the support vectors 4 Kernel based SVM By far, one of our assumption is that the training data can be separated linearly. Nevertheless in the data, as demonstrated in Fig. 4. The basic idea of kernel method is to make linear model work in nonlinear settings by introducing kernel functions. In particular, by mapping the data into a higher-dimensional example again. Consider a 2-dimensional input space (i.e., the original feature space), we define a kernel function K that takes x = (x1, x2) and z = (z1, z2) as inputs K(x, z) = (xT z)2 = (x1z1 + x2z2)2

where S denotes the indices of the support vectors Feng Li (SDU) SVM December 28, 2021 39 / 82 Kernel Methods Motivation: Linear models (e.g., linear regression, linear SVM etc.) cannot reflect the 2021 46 / 82 Kernels as High Dimensional Feature Mapping Let’s assume we are given a function K (kernel) that takes as inputs x and z K(x, z) = (xTz)2 = (x1z1 + x2z2)2 = x2 1z2 1 + x2 2z2 2 + 2x1x2z1z2 implicitly defines a mapping φ to a higher dim. space φ(x) = {x2 1, √ 2x1x2, x2 2} Simply defining the kernel in a certain way gives a higher dim. mapping φ The mapping does not have to be explicitly computed

December 28, 2021 1 / 46 Outline 1 Clustering 2 K-Means Method 3 K-Means Optimization Problem 4 Kernel K-Means 5 Hierarchical Clustering Feng Li (SDU) K-Means December 28, 2021 2 / 46 Clustering Usually badly if the clusters have non-convex shapes Kernel K-means or Spectral clustering can handle non-convex Feng Li (SDU) K-Means December 28, 2021 26 / 46 Kernel K-Means Basic idea: Replace the Euclidean k(µk, µk) − 2k(xi, µk) where k(·, ·) denotes the kernel function and φ is its (implicit) feature map Feng Li (SDU) K-Means December 28, 2021 27 / 46 Kernel K-Means Note: φ does not have to be computed/stored

Android device. The transformers which leverage the low rank methods and kernel approximations are grouped under Low Rank/Kernel group. Figure 4-19: Taxonomy of efficient transformers, depicting the various over this input using n kernels of dimensions (dk, dk, m) where dk is the spatial dimension of each kernel. The regular convolution operation with a single stride produces an output with dimensions (h, w operation requires h x w x n x dk x dk x m operations. Figure 4-20: Depiction of input, output and kernel shapes for a regular convolution with single stride. 29 Howard, Andrew G., et al. "Mobilenets: Efficient

padding='same', activation='relu', kernel_regularizer=reg)( x) x = layers.BatchNormalization()(x) x = layers.Conv1D( 32, (9), padding='same', activation='relu', kernel_regularizer=reg)( x) x = layers padding='same', activation='relu', kernel_regularizer=reg)(x) x = layers.BatchNormalization()(x) x = layers.Conv1D( r(64 * w), (9), padding='same', activation='relu', kernel_regularizer=reg)(x) x = layers padding='same', activation='relu', kernel_regularizer=reg)(x) x = layers.BatchNormalization()(x) x = layers.Conv1D( r(128 * w), (9), padding='same', activation='relu', kernel_regularizer=reg)(x) x = layers